arXiv subjects

Erick R. Castro

Publications and source records attributed to Erick R. Castro.

3 recordsLinked to original sources

arXiv2024

Subtle Nuances between Quantum and Classical regimes

This study explores the semiclassical limit of an integrable-chaotic bosonic many-body quantum system, providing nuanced insights into its behavior. We examine classical-quantum correspondences across different interaction regimes of bosons in a triple-well potential, ranging from the integrable to the self-trapping regime, and including the chaotic one. The close resemblance between the phase-space mean projections of classical trajectories and those of Husimi distributions evokes the Principle of Uniform Semiclassical Condensation (PUSC) of Wigner functions of eigenstates. Notably, the resulting figures also exhibit patterns reminiscent of Jason Gallas's "shrimp" shapes.

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arXiv2024

From integrability to chaos: the quantum-classical correspondence in a triple well bosonic model

In this work, we investigate the semiclassical limit of a simple bosonic quantum many-body system exhibiting both integrable and chaotic behavior. A classical Hamiltonian is derived using coherent states. The transition from regularity to chaos in classical dynamics is visualized through Poincaré sections. Classical trajectories in phase space closely resemble the projections of the Husimi functions of eigenstates with similar energy, even in chaotic cases. It is demonstrated that this correlation is more evident when projecting the eigenstates onto the Fock states. The analysis is carried out at a critical energy where the eigenstates are maximally delocalized in the Fock basis. Despite the imperfect delocalization, its influence is present in the classical and quantum properties under investigation. The study systematically establishes quantum-classical correspondence for a bosonic many-body system with more than two wells, even within the chaotic region.

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arXiv2023

Improving the convergence of an iterative algorithm for solving arbitrary linear equation systems using classical or quantum binary optimization

Recent advancements in quantum computing and quantum-inspired algorithms have sparked renewed interest in binary optimization. These hardware and software innovations promise to revolutionize solution times for complex problems. In this work, we propose a novel method for solving linear systems. Our approach leverages binary optimization, making it particularly well-suited for problems with large condition numbers. We transform the linear system into a binary optimization problem, drawing inspiration from the geometry of the original problem and resembling the conjugate gradient method. This approach employs conjugate directions that significantly accelerate the algorithm's convergence rate. Furthermore, we demonstrate that by leveraging partial knowledge of the problem's intrinsic geometry, we can decompose the original problem into smaller, independent sub-problems. These sub-problems can be efficiently tackled using either quantum or classical solvers. While determining the problem's geometry introduces some additional computational cost, this investment is outweighed by the substantial performance gains compared to existing methods.

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